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In integrating collaborative work in our approach to K-12 education, we are teaching students the benefit of listening, learning from others, coming to consensus on ideas, and other group dynamics. These are all essential skills in group problem solving exercises in school, and in adult project based work. What we should not lose sight of is both valuing the individual as a contributor, and building personal communication skills thereby promoting effective group dialogue and collaboration. It takes a very skilled teacher to nurture the individual as a person of abilities, aptitudes, and evolving capacity while at the same time teaching effective group dynamics. Productive group work is predicated upon individual skills in communication, and group skills in collaboration. We want children to know that their opinions and observations are highly valued, we want them to have the skills to communicate them effectively, and we develop collaborative skills to make project based learning effective.

In early development of these skills, it may well be the case that using physical manipulatives in the classroom facilitates the development of communication skills across curriculum topics. As personal skills in, for example, vocabulary, persuasion, reasoning, and advanced thinking develop, children could use manipulatives to assist them in communicating their ideas with peers. This is evidenced in the example of Kim Haines, 4th grade teacher at Dawson School in Lafayette, CO who used the INTOOBA Construction Kit in developing communication skills in listening, giving directions, providing clarification, and in either being a giver or receiver of information in her math class:

Essentially, teachers can observe individual thinking and development of these essential skills through the use of manipulatives while also noting the child’s functioning within a collaborative setting. Children here are supported in the learning of specific collaborative language through the use of their hands.

BLUE EGG ADVISORY GROUP, LLC are very pleased to announce the launch of the Intooba construction kit for K-6 math and STEAM education. This innovative product enhances the creativity and learning of students in these grades.

Modern children so seldom see the process of how something is made. They do not interact with authors as they delve into the writing process, nor do they do not see barns being constructed or crops being grown. They therefore miss out on the often-tedious tasks undertaken from idea to completed product. All interactions, production, thought processes, and output of any nature goes through a system and process. It is important for students to be able to think through what systems and processes are, how they are best defined, and how they might best be illustrated. This assists young learners in being observant of the world around them, questioning of how their environment operates, and being able to illustrate a written observation. The student handout is shown hereunder:

SYSTEMS AND PROCESSES

Systems and processes refer to the way the world around us operates. You may not have considered this before, but there are many such systems and processes all around us every day. Consider how the human brain controls our body motions, and vital functions. This is a system and a process. The system is the human body, and the process is the way the brain does this management. Other systems and processes, many of them man-made, include transportation systems, presidential debates, and how people get educated. A very simply system and process is how to make a cup of coffee. The system is the coffee beans are grown, prepared, and shipped to shops. The process is how you actually make a cup of coffee, or buy it.

Each of these follows a set of guidelines or procedures which usually occur in a sequence if they are to be successful. For example, consider the NYC subway system. It is a very complicated underground train system that allows millions of people to move around New York City quickly and efficiently. The system is the tracks and trains. The process is how people use it, including using a diagrammatic representation allowing people to see how to get from one place to another. You can Google it. Different colored lines represent different subway lines. So, it is a system, and process with a diagram.

Your task: 10 systems and processes. Write what they are (system), how they work (process), and try to draw a diagram of them. Please investigate 3 by yourself in class, 2 with a partner in class, 3 by yourself for homework, and 2 with an adult at home.

There is a tendency among younger children to compartmentalize what they have learned in each discipline, and not to stretch one piece of learning into another discipline. A very interesting and engaging project is to ask the children to become travel agents, and plan a vacation trip of their own. In this way, students learn to navigate the quite complicated world of airline and hotel websites, choose destinations based on political safety, convert currencies, look at maps, research cities/destinations on the web, plan a budget, and learn something about a country or region. Asking children to do all this in a single project engages them fully in the learning process, and brings mathematics into geography, technology into budgeting and so on. Later, children can use these research skills in many ways on other projects. The joy of early learning is to master adaptable skills which are useful throughout life, but particularly as they progress through their formal learning environment.

TRAVEL PROJECT # 1

You are to become a travel agent. Book your ideal holiday vacation to a destination of your choice. You must give an itemized budget for your trip. Total available dollars: $8000.00

You may consider yourself a single adult for the purposes of this exercise.

You need to:

(1) Decide which time of year you will be traveling
(2) Find an airline. Ascertain rates for travel.
(3) Find a hotel. Get rates for thirteen or fourteen nights.
(4) Find what you will be doing and eating. Include in budget.

You need to write an essay on your project. Be sure to include:

History and geography of the place you are visiting
Write a detailed budget
Find an example of the following:
An artist
A politician
A mathematician or scientist

Describe something about their life or work. What contribution did they make to society? How does their work impact you?

Travel Project # 2

Travel to the Seven Wonders of the Ancient World using the least amount of money, and in the shortest amount of time.

CONCEPT: To find new and creative ways to teach and learn mathematics.

PURPOSE: The concept here is to engage students in an interested and engaging way to learn mathematics. Smells are assigned numbers. Problems are formulated substituting smells for numbers. Students smell the problems, and solve them numerically.

MATERIALS:

Extracts: Depending on the complexity of the problems undertaken, purchase up to ten different extracts from the supermarket. These will represent 0-9. It is advisable to start more modestly, and purchase six extracts giving 1-6. In this way, students become familiar with the actual smells (orange, banana, vanilla etc.)

Paper: One large blank sheet per group. Several smaller problem solving sheets of blank or graph paper per group.

Clip boards: One per group

Markers: Expo marker for writing on the board. Regular marker for setting up the problem on the large white paper.

Two-sided tape

Paper napkins

Pencils

PROCEDURE:

In this lesson, we are doing two digit by two-digit multiplication. Teach the students a traditional example. 34 X 21. Solve it with them.

Explain to the students that today they will be smelling various smells, and that these smells will be associated with a number which you will write on the board.

In a first attempt, write the numbers 1-6 on the board. Next to each number, assign a smell to a number. 1 – banana, 2- coconut.

Ask the students to come and smell the smells in their groups.

On the large piece of paper, outline where the scented napkins will go, make an “X” indicating multiplication in the appropriate place, and draw a line indicating a multiplication problem.

Ask the groups to formulate and solve their own problems.

The teacher circulates around the room to the different groups, puts the selected scents on the paper napkins and affixes the napkins to the large white paper with the double-sided tape.

The students go around the room with their clipboards and paper and they smell each problem. They solve them numerically.

The teacher asks groups to provide the solution to other groups’ work. Then the teacher asks each group if that was indeed their work.

As a follow up activity, the teacher may ask students to create their own problems using smells.

NOTE: to ask students to provide an answer in smell format, fully ten smells need to be provided.

What would the world look like if people were allowed to speak only 20,000 words per year? Could we communicate effectively? What communication channels would suffer as a result of this change, and what channels would get increased use?

I have found it extremely useful to assist children to think of themselves as independent people. Quite obviously, pre-adolescent children are not independent in many respects, but creating an environment where they think of themselves as independent opens doors to many positive outcomes in the classroom. An independent young person is responsible for personal thoughts and actions, assignment planners, and homework. A vital and shared component of all these, and other, activities is the ability and responsibility to make decisions. Establishing oneself as a decision maker sets the stage for life as an independent person.

A very useful activity to undertake on the first day of school is to provide students with a blank sheet of paper approximately 18 inches long by 12 inches wide. On the board in front of the class write the word BORN with a period under it. Proceed to explain to the children that you want them to make a DECISION TREE outlining all the important decisions they have made in their lives to date. A decision tree will have branches for paths both taken and not taken. Paths not taken will end there, and paths taken lead to a continuation down the decision tree of life to the present day. It is imperative not to give too many ideas to the students at this point as to what specifically constitutes an important decisions. Of necessity for the purposes of this exercise, students should be thinking carefully through what decisions they think they have made over the course of their lives to date. Leaving it very open-ended without much guidance tends to produce varied and interesting results. Such results might include what school they ‘chose’ to go to from amongst alternatives they have heard of, what instruments or after-school activities they chose to do, or possibly where they have lived if they have moved apartments or cities. Whether they themselves actually made these decisions is immaterial. What is important is for them to think about making decisions, and to have some defined course they followed over their young lives. They should see that a large part of our human experience is essentially selecting from amongst a series of options. Once you establish yourself as a decision maker, then you are an independent person with regard to thought and responsibility for actions.

At times, one could give a few hints to those individuals who are struggling with the project in order to get them into a productive mode of thinking through this exercise. Once all students have finished this project, have students share their thoughts and ideas with each other. Studying the Robert Frost poem, The Road Not Taken at this juncture would be a very useful exercise.

After completing and discussing the poem, ask the students to turn over the sheet of paper upon which they have outlined their major life decisions to date. Again go the classroom board and write the word FUTURE on it with a period under it. Explain again the concept of a DECISION TREE to the students. This time, however, ask them to put together a set of possible scenarios of major decisions they think they will make for the remainder of their lives. Leave this discussion as vague as possible in order to foster creativity. Interesting outcomes here have been college, marriage, career(s), vehicles, sports, number of children, retirement, travel and in some instances even death. Here again, we are establishing the concept of independence through the ability to make decisions.

It is fascinating to see how children convert the written word into a visual representation, and vice versa. It certainly enriches the reading experience to be able to create vivid mental representations of what one is reading. Practicing drawing and reading/writing together could create an awareness of the process of transferring the written word into mental images, enhance descriptive abilities, and support creative and imaginative writing.

Journal topic 2:

Provide a scenic written passage from a well-known author, and ask the children to draw the scene in their writing journals.

Students can journal on the process they undertook to complete this assignment.

Journal topic 3:

Provide a colorful postage stamp to students. Ask them to place it in the center of a facing page, and expand the scene in the stamp with colored pencils. They can then write a story about their creation.

Point out to students that information can to transferred from words to images, and vice versa. Providing a detailed description of your ideas to readers help them make an accurate visual representation in their minds as they read your work. Similarly, reading detailed work helps the readers create captivating visual images.

All information which we receive into the brain for processing comes from one of our five senses. Developing an ability to effectively and efficiently apply as many of these senses as possible to a problem or investigation can only assist us in finding solutions to our queries. Many lessons can be developed and taught with this idea in mind.

Learning the process of active listening, for example, as opposed to passive listening or merely hearing, can assist students tremendously as they take in information for processing. Really listening to what is being said, with an active engagement, can facilitate an intake of all the information presented. Here is an example of a lesson promoting active listening in mathematics.

Procedure: Students are given small erasable writing tablets, erasable markers, and board erasers. They are told that this is a listening exercise. Not only is this lesson about listening carefully to the information presented; students also have to separate relevant information from the irrelevant material as well. Lastly, they have to decide how they will record the information as the reader proceeds with the statement and questions.

The teacher states that the problem will be read only once. A clear and precise statement is made as to what type of problem is being address whether it is, for example, time or distance. Students have to decide how they will record the information, look for relevant material, and solve the problem. A word problem is then slowly, carefully and methodically read to the students. At no point is any part of the problem communicated in written form. Students need to listen for relevant information, and undertake to solve the questions posed.

It is fascinating to see how students approach this form of questioning at first. Usually, most students begin by writing down everything the teacher says verbatim. In later exercises, students tend to make a simple diagrammatic chart to solve the problem.

Example:

Teacher states: this is a distance question.

A man decides to take a hike along the Appalachian Trail. This is a three-day adventure. On the first day, he walks 30 miles. The food he consumes that day costs $5.45. On the second day, he makes good progress. He saw two bears, and three Blue Jays. This day, he walks 25 miles. He stepped off the trail to buy water for $2.50. The final leg of his journey took him another 23 miles. He ate three cereal bars costing $3.00 each.

Question:

How many miles did he walk in total on this specific journey?

At this juncture, the teacher might also ask students to write down, on a separate piece of paper, how much he spent in total to see which students were actively listening to the entire story, and who listened only for distance information. The story can then be re-read, and the spending question asked again. Students and teacher can compare notes on the their answers.

The lesson then can be focused on a discussion of active learning, sorting of information for relevancy, and storage of additional information that may later become relevant. Students will also learn how most efficiently to record what they have heard.

Additional, more complicated, problem:

No information is written down by the teacher for the students to see.

Teacher states that this is a distance, time and expenditure question:

Judy was training for a marathon on Sunday. On Wednesday, she started running at 6:00 am. She ran 15 miles, finishing at 8:37 am. The next day, she ran 17 miles, starting at 6:00 am, and ending 2 hours and 47 minutes later. Conveniently, this practice run ended at the convenience store. There, Judy bought two vitamin waters, each costing $2.50, an energy shake costing $3.99, and a bag of potato chips at $2.99.